Solve Trigonometric Inequality sin x < cos x Graphically

Example on how to solve a trigonometric inequality graphically corresponding to question 5 in trigonometry_2.

Example 1


Over which of the following intervals is $\sin x<\cos x$?

  1. $(0 , \dfrac{\pi}{4})$

  2. $(\dfrac{\pi}{4} , \dfrac{\pi}{2})$

  3. $(\dfrac{\pi}{2} , \dfrac{3\pi}{4})$

  4. $(\dfrac{3\pi}{4} , \pi)$

  5. $(\pi , \dfrac{5\pi}{4})$

Solution


  1. This question could easily be answered by comparing the graphs of $y=sin x$ and $y=\cos x$. The two graphs are shown below and it easily seen that $y=\sin x$ is less than $y=\cos x$ over the open interval $(0,\dfrac{\pi}{4})$




    3. Answer A